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Popular Calculus Problems

derivative of f(x)= 1/((2x^3))	derivative\:f(x)=\frac{1}{(2x^{3})}
limit as x approaches 5 of 2/((x-5)^3)	\lim\:_{x\to\:5}(\frac{2}{(x-5)^{3}})
derivative of 2-4x	\frac{d}{dx}(2-4x)
integral of 1/(sqrt(4x^2+2))	\int\:\frac{1}{\sqrt{4x^{2}+2}}dx
y^{''}+6y^'+25y=0,y(0)=2,y^'(0)=-10	y^{\prime\:\prime\:}+6y^{\prime\:}+25y=0,y(0)=2,y^{\prime\:}(0)=-10
derivative of (6x/(1+3x^2))	\frac{d}{dx}(\frac{6x}{1+3x^{2}})
limit as x approaches 0 of 1/x ln(1+x)	\lim\:_{x\to\:0}(\frac{1}{x}\ln(1+x))
integral from 0 to pi of t^2e^{-st}	\int\:_{0}^{π}t^{2}e^{-st}dt
area y=e^x,y=e^{-x},x=1	area\:y=e^{x},y=e^{-x},x=1
derivative of xe^{-5x}	derivative\:xe^{-5x}
integral of (x^3+3x^2+6)/(x^2+2)	\int\:\frac{x^{3}+3x^{2}+6}{x^{2}+2}dx
integral of x/((x^2+4))	\int\:\frac{x}{(x^{2}+4)}dx
integral of sqrt(4+3x)	\int\:\sqrt{4+3x}dx
(\partial)/(\partial x)(x+sin(y+z))	\frac{\partial\:}{\partial\:x}(x+\sin(y+z))
derivative of 5+2x-7x^3	derivative\:5+2x-7x^{3}
derivative of 1/(2x^2+(x^4)/(16))	\frac{d}{dx}(\frac{1}{2x^{2}}+\frac{x^{4}}{16})
derivative of (x^2-sqrt(x)+3/4 x^4^2)	\frac{d}{dx}((x^{2}-\sqrt{x}+\frac{3}{4}x^{4})^{2})
y^'=(6x^2+y^2)/(xy)	y^{\prime\:}=\frac{6x^{2}+y^{2}}{xy}
integral of ye^{xy}	\int\:ye^{xy}dx
integral of xsqrt(5x+1)	\int\:x\sqrt{5x+1}dx
y^'=((e^{x-y}))/(1+e^x),y(1)=0	y^{\prime\:}=\frac{(e^{x-y})}{1+e^{x}},y(1)=0
limit as x approaches 2+of 2x-[\|x\|]	\lim\:_{x\to\:2+}(2x-[\left\|x\right\|])
limit as x approaches 0 of ((x^2+x))/x	\lim\:_{x\to\:0}(\frac{(x^{2}+x)}{x})
integral of (ln(x))/(sqrt(2x+3))	\int\:\frac{\ln(x)}{\sqrt{2x+3}}dx
(\partial)/(\partial x)(\sqrt[3]{(y-5x)^2})	\frac{\partial\:}{\partial\:x}(\sqrt[3]{(y-5x)^{2}})
limit as x approaches 2 of (x^2-9)/(x+2)	\lim\:_{x\to\:2}(\frac{x^{2}-9}{x+2})
(\partial)/(\partial x)(e^{sqrt(xy)})	\frac{\partial\:}{\partial\:x}(e^{\sqrt{xy}})
derivative of 4/((x+4^2))	\frac{d}{dx}(\frac{4}{(x+4)^{2}})
t*(dy)/(dt)=t^3+22t^3y	t\cdot\:\frac{dy}{dt}=t^{3}+22t^{3}y
derivative of y= x/(ln(x))	derivative\:y=\frac{x}{\ln(x)}
integral of sqrt(sec^2(x)-1)	\int\:\sqrt{\sec^{2}(x)-1}dx
integral of 1/(4x-x^2)	\int\:\frac{1}{4x-x^{2}}dx
derivative of arctan(2x+1)	\frac{d}{dx}(\arctan(2x+1))
limit as x approaches infinity of e^1	\lim\:_{x\to\:\infty\:}(e^{1})
derivative of x^2-4x+9	\frac{d}{dx}(x^{2}-4x+9)
y^{''}+4y^'+4y=e^{-2x}+x^2	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=e^{-2x}+x^{2}
(dy)/(dx)=13x^{12}y	\frac{dy}{dx}=13x^{12}y
y^'+y/((2+3t))=3	y^{\prime\:}+\frac{y}{(2+3t)}=3
derivative of arcsin((x-2/1))	\frac{d}{dx}(\arcsin(\frac{x-2}{1}))
integral of 1/(x(1+ln^2(x)))	\int\:\frac{1}{x(1+\ln^{2}(x))}dx
integral from 2 to 6 of pi(y-2)2	\int\:_{2}^{6}π(y-2)2dy
tangent of f(x)=5sqrt(x),\at x=16	tangent\:f(x)=5\sqrt{x},\at\:x=16
y^{''}+2y^'+y=2e^{-t}	y^{\prime\:\prime\:}+2y^{\prime\:}+y=2e^{-t}
longdivision (x+2)/(x-1)	longdivision\:\frac{x+2}{x-1}
(dy)/(dx)=(cos(5x))/(e^{5y)}	\frac{dy}{dx}=\frac{\cos(5x)}{e^{5y}}
integral of (2e^{2x})/(1+e^{2x)}	\int\:\frac{2e^{2x}}{1+e^{2x}}dx
y(dy)/(dx)=2x(64+y^2)	y\frac{dy}{dx}=2x(64+y^{2})
derivative of-(3x/y)	\frac{d}{dx}(-\frac{3x}{y})
limit as x approaches-2+of x/(x^2-4)	\lim\:_{x\to\:-2+}(\frac{x}{x^{2}-4})
tangent of 3x^2+4x+1	tangent\:3x^{2}+4x+1
derivative of x/(2x-1)	\frac{d}{dx}(\frac{x}{2x-1})
(dy)/(dt)=-4y	\frac{dy}{dt}=-4y
integral of 100x	\int\:100xdx
derivative of 4pir^2	derivative\:4πr^{2}
derivative of 2^{3x}	derivative\:2^{3x}
derivative of (5+4x)e^{-5x}	derivative\:(5+4x)e^{-5x}
derivative of tan(6x+x^{-4})	\frac{d}{dx}(\tan(6x)+x^{-4})
integral of cos(x)*e^{sin(x)}	\int\:\cos(x)\cdot\:e^{\sin(x)}dx
derivative of x-1/3 x^3	\frac{d}{dx}(x-\frac{1}{3}x^{3})
integral of x/(sqrt(x+10))	\int\:\frac{x}{\sqrt{x+10}}dx
integral from 0 to x of (e^{t^2}-1)/t	\int\:_{0}^{x}\frac{e^{t^{2}}-1}{t}dt
sum from n=1 to infinity of (n^5)/(3^n)	\sum\:_{n=1}^{\infty\:}\frac{n^{5}}{3^{n}}
integral of sec(x)(tan(x)+cos(x))	\int\:\sec(x)(\tan(x)+\cos(x))dx
3y^'=(3x*y+18x^2+2y^2)/(x^2),y(1)=3	3y^{\prime\:}=\frac{3x\cdot\:y+18x^{2}+2y^{2}}{x^{2}},y(1)=3
tangent of f(x)=x^4(3-x)^2,\at x=1	tangent\:f(x)=x^{4}(3-x)^{2},\at\:x=1
(dy)/(dx)=200-(3y)/(100-10x)	\frac{dy}{dx}=200-\frac{3y}{100-10x}
derivative of f(x)=4x^2+7x	derivative\:f(x)=4x^{2}+7x
derivative of (x-2(x+3))	\frac{d}{dx}((x-2)(x+3))
derivative of (4x^{ln(4x)})	\frac{d}{dx}((4x)^{\ln(4x)})
derivative of 25^{1/3}x^{2/3}	derivative\:25^{\frac{1}{3}}x^{\frac{2}{3}}
derivative of f(x)=tan(x)+5	derivative\:f(x)=\tan(x)+5
integral from 0 to 10 of 3x^2-42x+135	\int\:_{0}^{10}3x^{2}-42x+135dx
implicit (dy)/(dx),y^2=x-y	implicit\:\frac{dy}{dx},y^{2}=x-y
derivative of f(x)=(x^3+1)/(sqrt(x^2+1))	derivative\:f(x)=\frac{x^{3}+1}{\sqrt{x^{2}+1}}
integral of tan(u)	\int\:\tan(u)du
(dy)/(dx)xy=4	\frac{dy}{dx}xy=4
limit as x approaches 2 of (x^3-8)/(x-4)	\lim\:_{x\to\:2}(\frac{x^{3}-8}{x-4})
limit as x approaches 6 of 4/(x-6)	\lim\:_{x\to\:6}(\frac{4}{x-6})
(d^2)/(dx^2)(tan(2x))	\frac{d^{2}}{dx^{2}}(\tan(2x))
derivative of f(x)=((2x^2-3x+1)^2)/4+2	derivative\:f(x)=\frac{(2x^{2}-3x+1)^{2}}{4}+2
sum from n=1 to infinity of (-x)^{n+1}	\sum\:_{n=1}^{\infty\:}(-x)^{n+1}
taylor 9ln(5-8x^2)	taylor\:9\ln(5-8x^{2})
(dy)/(dt)=3+2y	\frac{dy}{dt}=3+2y
tangent of y=x^3-3x-4	tangent\:y=x^{3}-3x-4
(dy)/(dx)=(2x(y-1))/(x^2+3),y(1)=9	\frac{dy}{dx}=\frac{2x(y-1)}{x^{2}+3},y(1)=9
integral of x/((x^2+1)^4)	\int\:\frac{x}{(x^{2}+1)^{4}}dx
laplacetransform 2t*cos(t)	laplacetransform\:2t\cdot\:\cos(t)
integral of 3tcos(2t)	\int\:3t\cos(2t)dt
limit as x approaches 8 of (\|8-x\|)/(8-x)	\lim\:_{x\to\:8}(\frac{\left\|8-x\right\|}{8-x})
integral of (x^2+1)/(x^2+2)	\int\:\frac{x^{2}+1}{x^{2}+2}dx
limit as x approaches 3-of (7-x)/(x-3)	\lim\:_{x\to\:3-}(\frac{7-x}{x-3})
integral of x/(sqrt(x^4-1))	\int\:\frac{x}{\sqrt{x^{4}-1}}dx
(\partial)/(\partial x)(x^2y-y^2+y^3x^2)	\frac{\partial\:}{\partial\:x}(x^{2}y-y^{2}+y^{3}x^{2})
integral of sqrt(1-4x)	\int\:\sqrt{1-4x}dx
derivative of cot^2(sin(θ))	derivative\:\cot^{2}(\sin(θ))
parity y=cos(sqrt(sin(tan(pix))))	parity\:y=\cos(\sqrt{\sin(\tan(πx))})
(dy)/(dx)=y^{(1/3)}	\frac{dy}{dx}=y^{(\frac{1}{3})}
integral from 0 to 7 of 7-x	\int\:_{0}^{7}7-xdx
integral of 1/(sqrt(x^2+2x+65))	\int\:\frac{1}{\sqrt{x^{2}+2x+65}}dx
integral of 3x^2(x-2)(x+3)	\int\:3x^{2}(x-2)(x+3)dx

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